From 0d4388b9d71763955768f3ffb7d5d6cb7e7f51e7 Mon Sep 17 00:00:00 2001
From: Justus Kuhlmann <j_kuhl19@uni-muenster.de>
Date: Wed, 24 Jul 2024 14:17:53 +0200
Subject: [PATCH] incorporate changes discussed on 23.7.

---
 talk.tex | 35 ++++++++++++++++++++++-------------
 1 file changed, 22 insertions(+), 13 deletions(-)

diff --git a/talk.tex b/talk.tex
index 0bd3789..ba1c5f6 100644
--- a/talk.tex
+++ b/talk.tex
@@ -35,7 +35,6 @@
 \keywords{Münster}
 
 \newcommand{\customcite}[1]{{\color{fu-blue}\citename{#1}{author}}, \citefield{#1}{journaltitle}, {\color{pantone315}\citeyear{#1}}}
-\addbibresource{"./My Library.bib"}
 \begin{document}
 	
 \begin{frame}[plain]
@@ -51,7 +50,13 @@
 % differences at sym point?
 % improvement at the symmetric point
 % example
-
+\begin{frame}
+	\frametitle{What is this all about?}
+	\begin{itemize}
+		\item working with exp. Wilson-clover fermions
+		\item massive $\Rightarrow$ at $N_{\rm f}=3$ symmetric point
+	\end{itemize}
+\end{frame}
 \begin{frame}
 	\frametitle{Relevance for further improvement and physics}
 	\begin{itemize}
@@ -72,13 +77,13 @@
 \begin{frame}
 	\frametitle{Determination of $\ca$}
 	\begin{itemize}
-		\item Schrödinger functional
-		\item used already \arxivtag{hep-lat/9609035} for $N_{\rm f} = 2$ \arxivtag{hep-lat/0503003} and std. Wilson-Clover $N_{\rm f} = 3$ \arxivtag{1502.04999}
-		\item from PCAC mass $m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca \frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca s$
+		\item in Schrödinger functional boundary conditions
+		\item similar in quenched \arxivtag{hep-lat/9609035}, $N_{\rm f} = 2$ \arxivtag{hep-lat/0503003} and std. Wilson-Clover $N_{\rm f} = 3$ \arxivtag{1502.04999}
+		\item from PCAC mass 
 	\end{itemize}
 	\vspace{.5cm}
-	$$m_{\rm PCAC}^{(0)} = m_{\rm PCAC}^{(1)}$$
-	$$\Leftrightarrow \ca =  - \frac{r^{(1)} - r^{(0)}}{s^{(1)} - s^{(0)}}$$
+	$$m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca \frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca s$$
+	$$m_{\rm PCAC}^{(0)} = m_{\rm PCAC}^{(1)}\quad\Leftrightarrow\quad\ca =  - \frac{r^{(1)} - r^{(0)}}{s^{(1)} - s^{(0)}}$$
 \end{frame}
 
 \begin{frame}
@@ -91,6 +96,9 @@
 			\item also include $\omega_{\rm b4} = {\rm cons.}\;,\quad\omega_{\rm b5} = -r^2~e^{-r/a_0}$
 		\end{itemize}
 		\item eigenvectors of boundary-to-boundary corr. func. $(F_1)_{i,j} = -\langle O(\omega_{{\rm b}i}) O'(\omega_{{\rm b}j})\rangle$ lead to eigenstates $\pi^{(0)}, \pi^{(1)}$
+		\vspace{.5cm}
+		\pause
+		\item project $f_{\rm A}$ and $f_{\rm P}$ onto the eigenstates of $F_1$
 		% Question: do we include all wavefunctions or just some?
 		% How does this interplay with the states that we achieve?
 		% Which is the optimal wf combination?
@@ -112,10 +120,10 @@
 			$L/a$ & $\beta$ & $\kappa_{1}\approx\kappa_{\rm cr}$ & $\kappa_{2}$ & $\kappa_{3}\approx\kappa_{\rm sym}$&$a$\\
 			\midrule
 			24&3.685&0.1396980&0.1395500&0.1394400&0.120\\
-			32&3.80&0.1392500&---&0.1389630&\\
-			40&3.90&0.1388562&0.1386148&0.1386030&\\
-			48&4.00&0.1384942&0.1384880&0.1382720&\\
-			56&4.10&0.1381410&0.1380000&0.1379450&\\
+			32&3.80&0.1392500&---&0.1389630&0.095\\
+			40&3.90&0.1388562&0.1386148&0.1386030&0.080\\
+			48&4.00&0.1384942&0.1384880&0.1382720&0.064\\
+			56&4.10&0.1381410&0.1380000&0.1379450&0.055\\
 			\bottomrule
 		\end{tabular}
 	\end{center}
@@ -142,10 +150,11 @@
 	\framesubtitle{Hit symmetric and critical point exactly}
 	\begin{itemize}
 		\item ensembles not exactly tuned
-		\item determine points of interest as in \openlat~ensembles
+		\item able to interpolate to the desired points due to two or three values per $\beta$
+		\item determine points of interest as in \openlat~ensembles \arxivtag{2201.03874}
 		\item define: $$\Phi^{\rm SF}_4 = \frac{3}{2}\,8t_0\,|m_{\rm eff}|\,m_{\rm eff}
 		\quad \Rightarrow \quad \Phi^{\rm SF}_4\bigm\lvert_{m_{0,{\rm cr}}} = 0\,,\;\Phi^{\rm SF}_4\bigm\lvert_{m_{0,{\rm sym}}} = 1.115$$
-		\item interpolate to the desired points
+		
 	\end{itemize}
 \end{frame}